Question

Really need these answers! Evaluate each of the following without using a calculator or computer. Show your work.
a. sin(arcsin(1/2) + arcos(1/2))
b. sec(arccos(-√3/2))
c. arctan(tan(3π/4))
d. tan(arctan(3π/4))

Answer 1

sin(arcsin(1/2) + arcos(1/2))
arcos(1/2)=pi/3
arcsin(1/2)=pi/6
pi/3+pi/6=pi/2
sin pi/2=1

Answer 2

arccos(-√3/2)= pi-arccos(√3/2)=pi-pi/6=2*pi/3
sec(2*pi/3)=\[-\sqrt{3}/2\]

Answer 3

c tan inverse cancels tan
ans=3*pi/4

Answer 4

similarly for d